- Docente: Maximiliano Sioli
- Credits: 6
- SSD: FIS/01
- Language: Italian
- Moduli: Maximiliano Sioli (Modulo 1) Tommaso Chiarusi (Modulo 2) Gabriele Sirri (Modulo 3)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2) Traditional lectures (Modulo 3)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Physics (cod. 8025)
Learning outcomes
At the end of the course students get knowledge of the main statistical tools used in high energy physics, with and without accelerators. The course is complemented with exercise and laboratory sessions.
Course contents
Concept of probability: axiomatic, combinatorial, frequentist and
subjective. Conditional probability. Statistical independence.
Bayes' theorem.
Random variables and probability density functions.
Multivariate distributions. Marginal and conditional densities.
Functions of random variables. Distribution moments: expectation
value, variance, covariance. Error propagation in the presence of
correlated variables.
Examples of probability distributions: Binomial, Multinomial,
Poisson, Exponential, Normal (multivariate), Chi-square,
Breit-Wigner, Landau.
Characteristic functions and their applications. Central Limit
Theorem.
Monte Carlo method: convergence criteria, law of large
numbers, calculation of integrals and their uncertainties. Random
number generators. Sampling a generic distribution.
Hypothesis testing. Simple hypotheses. Efficiency and power of
the test. Neyman-Pearson lemma. Linear test, Fisher's discriminant.
Multivariate methods: Neural Networks, Boosted Decision Tree,
k-Nearest Neighbor. Statistical significance. P-values.
Look-Elsewhere Effect. Chi-square method for hypothesis
testing.
Generalities on statistical estimators. Test statistics and
estimators. Estimators for the expectation value, variance and
correlation. Variance of the estimators. The maximum likelihood
method. Score and Fisher information. Multi-parametric estimator
uncertainties with correlations. Extended Maximum Likelihood.
Bayesian estimators, Jeffrey's priors. Least squares method.
Exact methods for the construction of confidence intervals.
Gauss and Poisson case. Unified approach. Bayesian method. CLs
method. Systematic errors and nuisance parameters in the
calculation of confidence intervals. Frequentist and Bayesian
methods.
Lab: Elements of C++ and ROOT. RooFit Workspace, Factory,
composite models, multi-dimensional models. Use of RooStats to
compute confidence intervals, Profile Likelihood, Feldman-Cousins,
Bayesian intervals, w/ and w/o nuisance parameters. Use of TMVA as
classifier, description of TMVAGui.
Readings/Bibliography
- Glen Cowan, Statistical Data Analysis, Oxford Univ. Press, 1998
- Frederick James, Statistical Methods in Experimental Physics, World Scientific, 2007
- G. D'Agostini, Bayesian reasoning in data analysis - A
critical introduction, World Scientific Publishing,
2003
- B. P. Roe, Probability and Statistics in Experimental Physics, Springer, 1992
Teaching methods
Frontal lessons, exercises and laboratory sessions with statistical tools to solve practical problems.
Assessment methods
Oral examinatons. Students will be asked to face a typical HEP problem from theoretical and practical point of views, also quoting software tools presented in the Lab part of the course.
Links to further information
http://www.bo.infn.it/~sioli/asd.htm
Office hours
See the website of Maximiliano Sioli
See the website of Tommaso Chiarusi
See the website of Gabriele Sirri